Dynamics of a nanomechanical resonator coupled to a superconducting single-electron transistor

We present an analysis of the dynamics of a nanomechanical resonator coupled to a superconducting single electron transistor (SSET) in the vicinity of the Josephson quasiparticle (JQP) and double Josephson quasiparticle (DJQP) resonances. For weak coupling and wide separation of dynamical timescales, we find that for either superconducting resonance the dynamics of the resonator is given by a Fokker-Planck equation, i.e., the SSET behaves effectively as an equilibrium heat bath, characterised by an effective temperature, which also damps the resonator and renormalizes its frequency. Depending on the gate and drain-source voltage bias points with respect to the superconducting resonance, the SSET can also give rise to an instability in the mechanical resonator marked by negative damping and temperature within the appropriate Fokker-Planck equation. Furthermore, sufficiently close to a resonance, we find that the Fokker-Planck description breaks down. We also point out that there is a close analogy between coupling a nanomechanical resonator to a SSET in the vicinity of the JQP resonance and Doppler cooling of atoms by means of lasers

Universal quantum fluctuations of a cavity mode driven by a Josephson junction

We analyze the quantum dynamics of a superconducting cavity coupled to a voltage biased Josephson junction. The cavity is strongly excited at resonances where the voltage energy lost by a Cooper pair traversing the circuit is a multiple of the cavity photon energy. We find that the resonances are accompanied by substantial squeezing of the quantum fluctuations of the cavity over a broad range of parameters and are able to identify regimes where the fluctuations in the system take on universal values.Comment: 5 pages, 4 figure

Quantum master equation descriptions of a nanomechanical resonator coupled to a single-electron transistor

We analyse the quantum dynamics of a nanomechanical resonator coupled to a normal-state single-electron transistor (SET). Starting from a microscopic description of the system, we derive a master equation for the SET island charge and resonator which is valid in the limit of weak electro-mechanical coupling. Using this master equation we show that, apart from brief transients, the resonator always behaves like a damped harmonic oscillator with a shifted frequency and relaxes into a thermal-like steady state. Although the behaviour remains qualitatively the same, we find that the magnitude of the resonator damping rate and frequency shift depend very sensitively on the relative magnitudes of the resonator period and the electron tunnelling time. Maximum damping occurs when the electrical and mechanical time-scales are the same, but the frequency shift is greatest when the resonator moves much more slowly than the island charge. We then derive reduced master equations which describe just the resonator dynamics. By making slightly different approximations, we obtain two different reduced master equations for the resonator. Apart from minor differences, the two reduced master equations give rise to a consistent picture of the resonator dynamics which matches that obtained from the master equation including the SET island charge.Comment: 22 pages, 4 figure

Iterative solutions to the steady state density matrix for optomechanical systems

We present a sparse matrix permutation from graph theory that gives stable incomplete Lower-Upper (LU) preconditioners necessary for iterative solutions to the steady state density matrix for quantum optomechanical systems. This reordering is efficient, adding little overhead to the computation, and results in a marked reduction in both memory and runtime requirements compared to other solution methods, with performance gains increasing with system size. Either of these benchmarks can be tuned via the preconditioner accuracy and solution tolerance. This reordering optimizes the condition number of the approximate inverse, and is the only method found to be stable at large Hilbert space dimensions. This allows for steady state solutions to otherwise intractable quantum optomechanical systems.Comment: 10 pages, 5 figure

Implicit attitudes among trainee and qualified clinical psychologists in the UK

Implicit attitudes are thoughts and feelings that occur outside of conscious awareness and are therefore difficult to acknowledge and control. Implicit attitudes have been shown to predict socially sensitive intergroup behaviour not predicted by self-reported (explicit) attitudes. Consequently, negative attitudes towards certain demographic groups (e.g. women, older people, minority ethnic groups, gay people) may contribute to persistent disparities in employment, criminal justice, education and healthcare. The role of clinical psychologists (CPs) in the UK is very varied and CPs may be involved in direct or indirect clinical work and service development; and may be employed in leadership positions within the NHS. Therefore, implicit attitudes among CPs may have wide-ranging implications. However, very few studies have explored implicit attitudes among applied psychologists and none have considered trainee (TCP) and qualified clinical psychologists in the UK. Eighty-one CPs, 143 TCPs and 86 members of the general population completed between 1 and 5 Implicit Associations Tests (IAT) and self-report measures of attitudes towards age, sexuality, skin-tone, weight and gender/career associations via an internet application. The results showed that negatively biased implicit attitudes towards non-dominant groups were present among CPs and TCPs to a similar degree to those observed in the general population. Conversely, all groups self-reported neutral or positive biases towards all non-dominant groups, except overweight people. All groups showed a similar degree of implicit and explicit pro-thin bias. These findings were not associated with participant age and did not vary by location or religion. The results have implications for clinical psychology service provision and therapy outcomes (particularly for overweight clients), sex disparities in leadership within the profession and education and training. The findings require replication in a more diverse and representative sample and further research is required to determine whether implicit biases among clinical psychologists predict subtle, unconscious discriminatory behavior in this group

Self-immolative linkers in polymeric delivery systems

There has been significant interest in the methodologies of controlled release for a diverse range of applications spanning drug delivery, biological and chemical sensors, and diagnostics. The advancement in novel substrate-polymer coupling moieties has led to the discovery of self-immolative linkers. This new class of linker has gained popularity in recent years in polymeric release technology as a result of stable bond formation between protecting and leaving groups, which becomes labile upon activation, leading to the rapid disassembly of the parent polymer. This ability has prompted numerous studies into the design and development of self-immolative linkers and the kinetics surrounding their disassembly. This review details the main concepts that underpin self-immolative linker technologies that feature in polymeric or dendritic conjugate systems and outlines the chemistries of amplified self-immolative elimination

Comment on "Evidence for Quantized Displacement in Macroscopic Nanomechanical Oscillators"

In a recent Letter, Gaidarzhy et al. [1] claim to have observed evidence for "quantized displacements" of a high-order mode of a nanomechanical oscillator. We contend that the methods employed by the authors are unsuitable in principle to observe such states for any harmonic mode